More graphing and graphs.

We first examined travel graphs. A travel graph is a graph showing the relationship between the distance traveled and the time taken. With a travel graph, we can calculate the average speed (total distance by total time), a speed for a particular period, measuring the total distance traveled, etc. When a travel graph has information about two objects (like two cars), we can further see when a faster catches a slower one, or when two cars meet, etc.

We then looked at solving system of linear equations by graphs. Here we talk about two linear equations with x and y variables and find a solution which satisfies both equations. On the graph, it should be the intersection point of the two lines representing the two linear equations. Of course, there are some special cases where there is no solution due to the two lines being parallel to each other, or there are infinite number of solutions when two lines are the same.

Lastly we examined the graphs for a quadratic equation, taking the form of y = ax^2 + bx + c. Here we just need to student to have a basic knowledge of the shape of a quadratic function, its symmetry axis, the existence of a maximum or minimum point.

Here is this week’s homework:

Page 40: #6, #7, #8, #9, #21, #22, #23, #24, #34, #35, #36

Today we went over problems involving financial transactions first.

Here we talk about profit (selling price – cost) and profit percentage (profit / cost), discounted price (usual price – discount percentage * usual price), interests. This is mainly the continuation of what we learned last week, about rate, ratio and percentage.

We move on to coordinate plane and representing ordered pairs in the coordinate plane, drawing graphs for linear equation with two variables, and how to use linear graph to solve simple problems.

Homework:

Page 26, #22 – #28

Page 38, #3, #4, #5, #16

For midterm exam results, I will communicate with each family individually this week.

Today we first cover the section for word problems leading to quadratic equations, question like find the number such that the sum of the number and its square is 156. We go from the given conditions to come up with a quadratic equation, solve it. With real world problem, we need to be care to pick the right answer as a quadratic equation can have two solutions, one is possible, the other can be impossible in the real world.

We move on to talk about rate, ratio and percentage, and the corresponding word problems.

Rate is used to describe how a quantity change with regard to another quantity. For example, a worker is paid $84 for 6 hours of work, we say that he is paid $14 for one hour, or at the rate of $14/h.

Ratio is used to compare the magnitude of two similar quantities. It indicates what fraction one quantity is of the other, or how many times one quantity is as much as the other. Here is an example: a sum of money is divided between X and Y in the ratio of 3:5. if X gets $x and Y gets $y, then we can write: x:y = 3:5, or x/y = 3/5, etc.

Percentage is a special fraction with one hundred as its denominator. For example, 15% = 15/100 = 0.15

There are quite some word problems involving rate, ratio, and percentage, and some of them can be challenging,. We talk about several examples in the classroom.

Homework:

Page 21: #27 – #32

Page 24: #2, #4, #5, #9, #12, #14, #18, #19, #21, #25